A number of applications exist in which an original digital image is printed with a printer at a given resolution and scanned with a scanner at a different (e.g., slightly finer) resolution and in a position that might be slightly rotated. For example, postal indicia typically begin as digital images that are printed onto a mailpiece by, for example, a mailer and that are later scanned with a scanner by, for example, a postal service such as the USPS. In addition, with the enactment of The Check Clearing for the 21st Century Act, which removed the legal requirement that an original paper check had to be presented to obtain payment, checks are more frequently being generated as digital images that are printed and then subsequently scanned and deposited as scanned images. The print-scan process that is performed in these and other similar circumstances transforms the original digital image into another digital image that typically has the same content as the original image as observed by human eyes. However, the print-scan process also introduces various distortions into the newly generated (scanned) image, such as geometric transformations (in particular rotation, scaling and translation) and pixel value changes due to, for example, blurring of adjacent pixels, gamma correction, etc., that cause it to differ from the original digital image. In many situations, such as reading small sized barcodes, it is advantageous to be able to reconstruct the original image from the distorted scanned image (resulting from a print-scan process) as accurately as possible. Reconstruction of the original digital image in this manner would greatly assist with a number of applications, including, without limitation, forensic analysis, copy and fraud detection, and increasing the readable density of printed information, among other things.
Current image reconstruction algorithms, while functional, are lacking as they do not take into account the position of the scanning grid used to scan the printed original image with respect to the printing grid used to print the original digital image. Such algorithms, while functional, thus lack a certain degree of accuracy. Furthermore, for black and white images scanned with a grey scale scanner, most current image reconstruction algorithms use a simple thresholding method and as a result do not yield satisfying results. Thus, there is a need for an improved method of reconstructing images in a situation where an original black and white image is printed with a grid printer (e.g., a dot matrix impact printer, an inkjet printer, or a thermal printer as opposed to an offset printer) and where the printed image is then scanned with a grey scale scanner having a resolution that may differ from the printer resolution.